Human leukocyte antigens (HLA) or histocompatibility molecules are glycoproteins that play a pivotal role in the development of an effective immune response. An important function of the HLA molecules is the ability to bind and present antigen peptides to T lymphocytes. Presently there is no comprehensive way of predicting and energetically evaluating peptide binding on HLA molecules. To quantitatively determine the binding specificity of a class II HLA molecule interacting with peptides, a novel decomposition approach based on deterministic global optimization is proposed that takes advantage of the topography of HLA binding grove, and examined the interactions of the bound peptide with the five different pockets. In particular, the main focus of this paper is the study of pocket 1 of HLADR1 (DRB1*0101 allele). The determination of the minimum energy conformation is based on the ECEPP/3 potential energy model that describes the energetics of the atomic interactions. The minimization of the total potential energy is formulated on the set of peptide dihedral angles, Euler angles, and translation variables to describe the relative position. The deterministic global optimization algorithm, alpha BB, which has been shown to be epsilon-convergent to the global minimum potential energy through the solution of a series of nonlinear convex optimization problems, is utilized. The PACK conformational energy model that utilizes the ECEPP/3 model but also allows the consideration of protein chain interactions is interfaced with alpha BB. MSEED, a program used to calculate the solvation contribution via the area accessible to the solvent, is also interfaced with alpha BB. Results are presented for the entire array of naturally occurring amino acids binding to pocket 1 of the HLA DR1 molecule and very good agreement with experimental binding assays is obtained.